Dai et al. [1]} proposed the deformable convolution network, where additional offsets were calculated to obtain information away from its regular local kernel neighborhood.
Zhu et al. [2]} further introduced a modulation mask to strengthen the capability of manipulating spatial support regions.
Let \(p_k\)  be the \(k\) -th sampling offset in a standard convolution with kernel size \(n\times n\) . For example, when \(n=3\) , we have \(p_k\in \lbrace (-1,-1),(-1,0),\cdots ,(1,1)\rbrace \) . We denote the \(k\) -th additional learned offset and mask at location \(p + p_k\)  by \(\Delta p_k\)  and \(\Delta m_k\)  respectively. A deformable convolution can be formulated as
\(F_{out}(p) = \sum ^{n^2}_{k=1}w(p_k)\cdot F_{in}(p+p_k+\Delta p_k)\cdot \Delta m_k(p),\) 
